I have never heard of any verse more quoted and memorized than this one. Many people know it without knowing a single other thing about Christianity.* If there was one verse we don't need to quote in a post this would be it, but here it is for reference anyway:

John 3:16 (ESV)
For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.

In fact you almost certainly didn't recognize those words since that's a new-ish translation. The one you memorized as a kid was probably NIV or KJV:

John 3:16 (KJV)
For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.

So what does it mean? Are there different interpretations or is the breadth of Christian tradition pretty much united on this one? Is the meaning so clear that people with no other context are able to understand it? Is it a secret code that you need a legend to understand? Most specifically what is the scope of the concepts of love, belief, and the world in this verse?

* True story. I asked a guy one time if he'd read the Bible. His answer was quote: "Oh ya you mean like the John 3:16 thing? Ya I've heard of it." When pressed if he knew what what the three and the sixteen had to do with it, he was shocked to learn that it was just a fragment of a larger text.

World

world: earth, world system, whole universe; adornment. In some contexts, the world is simply the place where people live, in other contexts (especially in John), the world is a system opposed to God

Interesting points: kosmos can be translated as the "whole universe". Also, note that in John it's considered a "system opposed to God" in some contexts.

Believe

The Apostolic Bible translates this as "trusting", as you can see. The actual word is πιστεύω (pisteuo).

From Strongs (4100)

to believe, put one's faith in, trust, with an implication that actions based on that trust may follow; (pass.) entrust

(emphasis added)

This is the key that I think you might be looking for. This isn't just as simple as saying "Yeah, I believe that Jesus died for me." This is to "put one's faith in". This is a more active belief.

Nonetheless, I believe that if someone truly has faith in Jesus that their life will be impacted by it. That's what separates out shallow "belief" from deep "belief". It's that deeper belief/faith/trust that is what God wants from us.